A Runge-Kutta type four-step method with vanished phase-lag and its first and second derivatives for each level for the numerical integration of the Schrodinger equation

被引：82

作者：

Alolyan, Ibraheem ^{[1
]}

Simos, T. E. ^{[1
,2
]}

机构：

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[2] Univ Peloponnese, Fac Econ Management & Informat, Dept Informat & Telecommun, Sci Computat Lab, Tripolis 22100, Greece

来源：

JOURNAL OF MATHEMATICAL CHEMISTRY | 2014年 / 52卷 / 03期

关键词：

Schrodinger equation; Multistep methods; Hybrid methods; Runge-Kutta type methods; Interval of periodicity; P-stability; Phase-lag; Phase-fitted; Derivatives of the phase-lag; TRIGONOMETRICALLY-FITTED FORMULAS; PREDICTOR-CORRECTOR METHOD; INITIAL-VALUE PROBLEMS; SYMMETRIC MULTISTEP METHODS; HYBRID EXPLICIT METHODS; LONG-TIME INTEGRATION; NUMEROV-TYPE METHOD; HIGH-ORDER; SYMPLECTIC METHODS; INTERNATIONAL-CONFERENCE;

D O I：

10.1007/s10910-013-0301-1

中图分类号：

O6 [化学];

学科分类号：

0703 ;

摘要：

The investigation of the impact of the vanishing of the phase-lag and its first and second derivatives on the efficiency of a four-step Runge-Kutta type method of sixth algebraic order is presented in this paper. Based on the above mentioned investigation, a Runge-Kutta type of two level four-step method of sixth algebraic order is produced. The error and the stability of the new obtained method are also studied in the present paper. The obtained new method is applied to the resonance problem of the Schrodinger equation the efficiency of the method to be examined.

引用

页码：917 / 947

页数：31

共 108 条

[1] A new four-step hybrid type method with vanished phase-lag and its first derivatives for each level for the approximate integration of the Schrodinger equation [J].

Alolyan, Ibraheem ;

Simos, T. E. .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2013, 51 (09) :2542-2571

[2] High order four-step hybrid method with vanished phase-lag and its derivatives for the approximate solution of the Schrodinger equation [J].

Alolyan, Ibraheem ;

Simos, T. E. .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2013, 51 (02) :532-555

[3] A family of exponentially-fitted Runge-Kutta methods with exponential order up to three for the numerical solution of the Schrodinger equation [J].

Anastassi, Z. A. ;

Simos, T. E. .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2007, 41 (01) :79-100

[4] A parametric symmetric linear four-step method for the efficient integration of the Schrodinger equation and related oscillatory problems [J].

Anastassi, Z. A. ;

Simos, T. E. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2012, 236 (16) :3880-3889

[5] Numerical multistep methods for the efficient solution of quantum mechanics and related problems [J].

Anastassi, Z. A. ;

Simos, T. E. .

PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2009, 482 :1-240

[6] A family of two-stage two-step methods for the numerical integration of the Schrodinger equation and related IVPs with oscillating solution [J].

Anastassi, Z. A. ;

Simos, T. E. .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2009, 45 (04) :1102-1129

[7] An optimized Runge-Kutta method for the solution of orbital problems [J].

Anastassi, ZA ;

Simos, TE .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 175 (01) :1-9

[8] Trigonometrically fitted Runge-Kutta methods for the numerical solution of the Schrodinger equation [J].

Anastassi, ZA ;

Simos, TE .

JOURNAL OF MATHEMATICAL CHEMISTRY, 2005, 37 (03) :281-293

[9]

[Anonymous], COMPUT LETT

[10]

[Anonymous], 1977, QUANTUM MECH NONRELA

← 1 2 3 4 5 6 7 8 9 10 →